Question

A(-1,3), B(5,2) and C(5,-2) arethe vertices of a triangle. (i)Find the coordinates of thecentroid G of the triangle(ii)Find the equation of the linethrough G and parallel to AC *​

Answer 1

Step-by-step explanation:

ANSWER

Given, A(−1,3),B(4,2),C(3,−2)

(i) Co-ordinates of centroid G is

G(x,y)=(

2

(x

1

+x

2

+x

3

)

,

2

(y

1

+y

2

+y

3

)

)

=(

3

(−1+4+3)

,

3

(3+2−2)

)

=(

3

6

,

3

3

)=(2,1)

Hence, the co-ordinates of the centroid G of the triangle is (2,1)

(ii) Slope of AC=

(x

2

−x

1

)

(y

2

−y

1

)

=

(3−(−1))

(−2−3)

=

4

−5

So, the slope of the line parallel to AC is also

4

−5

Now, the equation of line through G is

y−1=(

4

−5

)(x−2)

4y−4=−5x+10

5x+4y=14

Thus, the required line equation 5x+4y=14.